Bone selection hidden in side view
Following the question, its comments and the answer from the OP, my though is this is not the axis mirror which leads to the situation (or please @BenMora explain a bit more).

Here is a setting with an operator derived from the script templates.

It's showing in blue the faces index, in green edges index and in red the index of vertices. We are here in face selection mode, but the same occurs whatever the mode is.



Element's index is a way to identify it in the mesh. To be simple, it is an integer designing the element (in a separated range for vertices, edges and faces). 

What is happening here (experimental conclusions):

In wireframe mode, Blender draws following the index. So bigger index is drawn over the smaller one.

And this is visibly the same for armatures.

To tell the truth, before this question, I've never noticed it... but thinking about it, I'm quite sure this is a wanted behavior for performance reason... maybe.

Please comment if this is to report to the Foundation in the bug tracker.